The objective of this study is to develop a better understanding of the effects of transient foundation uplift on response of structures, so that the related reduction in earthquake forces can be considered in design of structures. The mathematical models chosen are simple, but incorporate the most important effects of soil flexibility and realistic mechanics of uplifting and impact. In its fixed base condition, the structure itself is idealized as a single-degree-of-freedom system attached to a flexibly supported rigid foundation mat. The flexibility and damping of the supporting soil are represented by two alternative idealizations; two spring-damper elements, one at each edge of the foundation mat, or Winkler foundation with spring-damper elements distributed over the entire width of the foundation mat.